The inherent problem associated with coherent QPSK systems is that of phase ambiguity at the receiver. This is due to the inability of the carrier recovery circuit to distinguish the reference phase from the other phase (or phases) of the received carrier. For QPSK system, there are eight possibilities of errors caused by the recovered carrier being at the wrong phase and also caused by phase rotation direction ambiguity (i.e., caused by the phase of the two channels being reversed) in the transmission medium.
For uncoded systems, the phase ambiguity problem can be resolved by using the differential encoding-decoding technique. However, that technique causes the decoded output to contain highly correlated errors (double-error phenomenon) since errors almost always occur in pairs. An alternate method of resolving the phase ambiguity problem in the coherent QPSK systems is to make use of the sync markers already existing in the framed data transmission.
For coded systems, the resolution of phase ambiguity becomes more involved. For example, with the conventional differential coding method implemented inside a forward error correcting (FEC) encoder and decoder pair, a burst or double error can occur, and the use of sync markers can result in the reduction of transmission efficiency.
For general discussion, phase ambiguity resolution techniques may be classified into two categories: differential coding technique, and nondifferential coding technique. For an uncoded QPSK system, a nondifferential coding technique known is a "unique-word detection" technique. For a coded system, there are two known techniques, a "threshold decoder" and "unique-word detection" technique. The following outlines these techniques.
A. Uncoded QPSK Systems PA0 B. Coded QPSK Systems PA0 (a) Type 1 error: I.sub.R =I.sub.T inverted, or I.sub.R =Q.sub.T inverted PA0 (b) Type 2 error: Q.sub.R =Q.sub.T inverted, or Q.sub.R =I.sub.T inverted PA0 (c) Type 3 error: I.sub.R and Q.sub.R channels are switched (reversed), e.g., I.sub.R =Q.sub.T or I.sub.R =Q.sub.T inverted, or Q.sub.R =I.sub.T or Q.sub.R =I.sub.T inverted.
1. Differential Coding PA1 2. Unique Word Detection PA1 1. Differential Coding PA1 2. Nondifferential Coding
a. Differential Inside Forward-Error-Correcting (FEC) with Encoder and Decoder Pair (codec) PA2 b. Differential Outside Forward-Error-Correcting (FEC) with Encoder and Decoder Pair (codec) PA2 a. Threshold Decoder PA2 b. Unique Word Detection
The differential coding technique for uncoded QPSK systems is well known and reported in literature. (W. J. Weber, "Differential Encoding for Multiple Amplitude and Phase Shift Keying Systems," IEEE Transactions on Communications, Vol. COM-26, No. 3, March 1978.) The differential encoder can be readily paired with a differential decoder at a receiver. The receiver resolves the phase ambiguities based on the difference between the detected symbol phases. Since the difference is independent of the locked-in phase, the four-phase ambiguity associated with each case (normal or reverse sense) disappears at the output of the decoder differential. This technique is very simple to implement and can be performed in the modem independently on any data acquisition equipments, but due to the "burst error" associated with this technique (one erroneously detected phase will cause two consecutive false symbols), the detection performance of the transmitted sync markers can be degraded seriously.
The unique-word detection technique was patented by C. J. Wolejsza and E. R. Cacciamani, "Phase-Ambiguity Resolution in a Four-Phase PSK Communications System," U.S. Pat. No. 3,736,507. It utilizes two unique words (sync words) separately modulated onto the two quadrature I and Q channels at the transmitter. Since there are eight possible combinations of two possible cases (as shown in the following table), each combination uniquely defines one phase ambiguity condition.
TABLE I ______________________________________ THE RELATIONSHIPS BETWEEN THE TRANSMITTED AND RECEIVED DATA Received Data Without Received Data With Phase Rotation Phase Rotation Carrier Direction Ambiguity Direction Ambiguity Phase Error (Normal Sense) (Reverse Sense) (Degree) I.sub.R Q.sub.R I.sub.R Q.sub.R ______________________________________ 0 I.sub.T Q.sub.T Q.sub.T I.sub.T 90 -Q.sub.T I.sub.T I.sub.T -Q.sub.T 180 -I.sub.T -Q.sub.T -Q.sub.T -I.sub.T 270 Q.sub.T -I.sub.T -I.sub.T Q.sub.T ______________________________________ Note: The negative sign indicates the complement of the data
Thus, each error appearing in the two data channels of the QPSK demodulator is uniquely defined by a particular phase error. The unique-word detection technique is used to correct the errors at the outputs of the channels by monitoring and detecting the true or compliment form of the two unique words. For example, if the two unique words detected are in their complement form, then the received data should be inverted (complemented).
It should be noted that this unique-word detection technique does not identify the phase error of the recovered coherent carrier which caused the errors, but corrects the errors caused by the phase errors without phase rotation at 90.degree., 180.degree. and 270.degree. phase error. The sync markers already existing in the framed data transmission can be used as the unique words for resolving the phase ambiguity. This unique-word detection technique also has the advantage of not excluding the use of forward-error-correcting (FEC) techniques. However, it is more complex than the differential encoding-decoding technique and requires a careful selection of a suitable pattern for the unique words in order to achieve a low probability of false detection. Another disadvantage is that it may increase the number of noninformation bits in the total data stream thereby increasing the bandwidth necessary to transmit a given amount of information.
As shown in the outline above, the differential coding technique for coded QPSK systems can be classified into two categories: (a) phase ambiguity resolution by differential coding inside forward-error-correcting (FEC) with encoder and decoder pair (codec); and (b) phase ambiguity resolution by differential coding outside FEC codec.
The scheme for differential coding inside an FEC codec has a serious degradation in the bit error rate due to the burst error. (G. G. Forney and E. K. Bower, "A High-Speed Sequential Decoder: Prototype Design and Test," IEEE Transactions on Communication Technology, Vol. COM-19, No. 5, October 1971.) This is because one erroneously detected phase will cause two consecutive false symbols (a burst error) even if the next phase is received correctly. This burst error can cause a bit error rate degradation of 3 dB.
The adverse effect of the "burst error" in differential coding inside the FEC codec can be eliminated by using the well known technique of interleaving symbols. (Y. Tsuji, "Phase Ambiguity Resolution in a 4-Phase PSK Modulation System with Forward-Error-Correcting Convolutional Codes," COMSAT Technical Review, Vol. 6, No. 2, Fall 1976.) This is because the even and odd symbols are encoded independently so that the effect of burst error is changed to random error in the data, thus avoiding degradation. However, it should be noted that without symbol interleaving, the use of the differential coding inside the FEC codec does not require synchronization time to eliminate the phase ambiguity for the error decoder. This technique can be used in either a burst signal mode or a continuous signal mode. With symbol interleaving, this differential coding inside an FEC codec does not degrade the capability of the FEC codec with simplified hardware.
When differential coding is used an FEC codec, the bit error rate degradation due to "burst error" can be avoided. This is because the error correcting decoder does not encounter the double-error phenomenon, and only the bit error rate of the error-correcting decoder is of concern. Note that this decoder output bit error rate is an improved bit error rate due to error correcting action. Doubling the decoder output error rate results in a smaller bit signal-to-noise ratio loss than doubling the input error rate because the curve of bit error rate versus bit signal-to-noise ratio is steeper for the decoder output.
It is important to note that phase ambiguity resolution by differential coding external to error-control coding is to be used together with the synchronizer circuit of the FEC decoder. However, the resolution performance depends on the synchronizer circuit of the FEC decoder. This technique is not suitable for application to burst mode operations due to the relatively long time necessary for resolving the phase ambiguity.
For systems using nontransparent codes that do not have phase rotation direction ambiguity, there is no need for differential encoding because the synchronizer itself can resolve the phase ambiguity. For systems that have both phase rotation direction ambiguity (reverse sense) and recovered carrier phase ambiguity (normal sense), differential coding is always required regardless of the type of codes used (transparent or nontransparent).
As noted in the outline above, there are two nondifferential coding techniques for phase ambiguity resolution, namely a threshold decoder technique and a unique-word detection technique. The threshold decoder technique makes up of a synchronizer circuit that is inserted between the output of the QPSK demodulator and the input of a threshold decoder of a type which can correct a predetermined number of bit errors in a coded stream. (A. S. Dohne and E. R. Cacciamani, "Phase Ambiguity Resolution System Using Convolutional Coding-Threshold Decoding," U.S. Pat. No. 3,806,647, Apr. 23, 1974.) This particular synchronizer performs both phase ambiguity resolution and node synchronization without using unique code words. This synchronizer includes a memory counter which has all possible combinations of errors caused by the phase ambiguity. This memory counter is controlled by correction pulses which are generated int he synchronizer by an error rate detector.
When the number of correction bits during a frame exceeds the number which would normally occur if the system were operating correctly without phase ambiguity and without incorrect node synchronization, the synchronizer assumes that there is a problem caused either by phase ambiguity or node synchronization. Each time this occurs, the error rate decoder generates correction pulses.
The correction pulses are used to advance the memory counter through its states. It will eventually reach the state which makes all needed corrections since all possible combinations of errors are stored in the memory counter. When all errors are corrected, there will no longer be errors in the bit stream applied to the threshold decoder, the search pulses will then no longer be generated, and the memory counter will remain in the state which provides all needed corrections.
The threshold decoder technique improves communications efficiency, i.e., requires less bandwidth to transmit a given amount of information. But since the synchronizer has to search for the correct state out of all possible combinations of errors caused either by the phase ambiguity or node synchronization, this technique may require a relatively long time for phase ambiguity resolution.
The unique-word detection technique has been described above in connection with an uncoded QPSK system and can be modified for use with a coded QPSK system. At the transmitter, the unique words are inserted in a message preamble after the data has been encoded, and at the receiver, the unique words are detected before the FEC decoder. This implementation will allow the system to correct the errors caused by the phase ambiguity as described in connection with an uncoded QPSK system.
In summary, one particularly well-known technique for resolving the phase ambiguity of QPSK systems utilizes two unique words that are separately modulated onto the quadrature channels at the transmitter. This technique proposes that errors associated with eight possible phase ambiguity conditions can be corrected by detecting the true or complement of two unique words that are separately modulated onto the two quadrature channels at the transmitter. Since there are eight possible phase ambiguity conditions, correction of all errors by this technique requires a rather complicated circuit to resolve the phase ambiguity. Another technique described by E. Cacciamani, et al., in IEEE Transactions on Communication Technology, Vol. COM-19, No. 6, December 1971, titled "Phase-Ambiguity Resolution in a Four-Phase PSK Communications System," proposed to resolve the eight possible phase ambiguity conditions for offset QPSK systems, herein referred to as OQPSK. However, that scheme requires that proper timing between the two unique words can be known precisely.
Although the problem of phase ambiguity can be resolved by the techniques mentioned above in QPSK modulation systems, when unique-word detection techniques are used, the demodulator and the unique-word detector in a OQPSK receiver needs to be designed to achieve better performance while minimizing the complexity of the receiver.